What is the value of 6cos(45)+3sec(45) ?

The value of 6cos(45)+3sec(45) is 6sqrt(2)

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6cos(45)+3sec(45)

6 cos (4 5^{\circ}) + 3 sec (4 5^{\circ})

62

Decimal Notation

8.48528 \dots

Solution steps

6 cos (4 5^{\circ}) + 3 sec (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 5^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= 6 \cdot \frac{2}{2} + 32

Simplify

6 \cdot \frac{2}{2} + 32 : 62

6 \cdot \frac{2}{2} + 32

6 \cdot \frac{2}{2} = 32

6 \cdot \frac{2}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 32

= 32 + 32

Add similar elements:

32 + 32 = 62

= 62

= 62

tan (arccos (- \frac{3}{2}) + π)

3 + 2 sin (\frac{π}{3})

cosh (0) - 1

2 sec^{2} (\frac{π}{2}) tan (\frac{π}{2})

\frac{1 - sin ( 3 0 ^{\circ} )}{1 + sin ( 3 0 ^{\circ} )}

What is the value of 6cos(45)+3sec(45) ?
The value of 6cos(45)+3sec(45) is 6sqrt(2)